'Tis yer ballvalve Mr Inc. If it runs continuously, then it probably has dirt in it, or it needs replacing.
Since it only happens at 5:30 am, then it's more likely to be the float level is set too high. All mains water pressures rise overnight because few people are using them. Turning on a hot tap simply drains some of the excess.
Grab the arm with one hand to steady it, then bend the lever down a little. That will turn the float downwards so that it cuts out at a lower level.
A bit of trial and error will get it right.